Topological band theory has been studied for free fermions for decades,and one of the most profound physical results is the bulk-boundary correspondence.Recently a focus in topological physics is extending topological...Topological band theory has been studied for free fermions for decades,and one of the most profound physical results is the bulk-boundary correspondence.Recently a focus in topological physics is extending topological classification to mixed states.Here,we focus on Gaussian mixed states for which the modular Hamiltonians of the density matrix are quadratic free fermion models with U(1)symmetry and can be classified by topological invariants.The bulk-boundary correspondence is then manifested as stable gapless modes of the modular Hamiltonian and degenerate spectrum of the density matrix.In this article,we show that these gapless modes can be detected by the full counting statistics,mathematically described by a function introduced as F(θ).A divergent derivative atθ=πcan be used to probe the gapless modes in the modular Hamiltonian.Based on this,a topological indicator,whose quantization to unity senses topologically nontrivial mixed states,is introduced.We present the physical intuition of these results and also demonstrate these results with concrete models in both one-and two-dimensions.Our results pave the way for revealing the physical significance of topology in mixed states.展开更多
Software module clustering is to divide the complex software system into many subsystems to enhance the intelligibility and maintainability of software systems. To increase convergence speed and optimize clustering so...Software module clustering is to divide the complex software system into many subsystems to enhance the intelligibility and maintainability of software systems. To increase convergence speed and optimize clustering solution,density PSO-based( DPSO) software module clustering algorithm is proposed. Firstly,the software system is converted into complex network diagram,and then the particle swarm optimization( PSO) algorithm is improved.The shortest path method is used to initialize the swarm,and the probability selection approach is used to update the particle positions. Furthermore,density-based modularization quality( DMQ) function is designed to evaluate the clustering quality. Five typical open source projects are selected as benchmark programs to verify the efficiency of the DPSO algorithm. Hill climbing( HC) algorithm,genetic algorithm( GA),PSO and DPSO algorithm are compared in the modularization quality( MQ) and DMQ. The experimental results show that the DPSO is more stable and more convergent than the other three traditional algorithms. The DMQ standard is more reasonable than MQ standard in guiding software module clustering.展开更多
This paper discusses a popular community definition in complex network research in terms of the conditions under which a community is minimal, that is, the community cannot be split into several smaller communities or...This paper discusses a popular community definition in complex network research in terms of the conditions under which a community is minimal, that is, the community cannot be split into several smaller communities or split and reorganized with other network elements into new communities. The result provides a base on which further optimization computation of the quantitative measure for community identification can be realized.展开更多
基金supported by the National Key R&D Program of China(Grant No.2023YFA1406702)the Innovation Program for Quantum Science and Technology 2021ZD0302005+1 种基金the XPLORER Prizepartly supported by the Start-up Research Fund of Southeast University(RF1028624190)。
文摘Topological band theory has been studied for free fermions for decades,and one of the most profound physical results is the bulk-boundary correspondence.Recently a focus in topological physics is extending topological classification to mixed states.Here,we focus on Gaussian mixed states for which the modular Hamiltonians of the density matrix are quadratic free fermion models with U(1)symmetry and can be classified by topological invariants.The bulk-boundary correspondence is then manifested as stable gapless modes of the modular Hamiltonian and degenerate spectrum of the density matrix.In this article,we show that these gapless modes can be detected by the full counting statistics,mathematically described by a function introduced as F(θ).A divergent derivative atθ=πcan be used to probe the gapless modes in the modular Hamiltonian.Based on this,a topological indicator,whose quantization to unity senses topologically nontrivial mixed states,is introduced.We present the physical intuition of these results and also demonstrate these results with concrete models in both one-and two-dimensions.Our results pave the way for revealing the physical significance of topology in mixed states.
基金supported by the special fund for key discipline construction of general institutions of higher learning from Shaanxi Province,and the Industrial Research Project of Shaanxi Province ( 2018GY - 014)
文摘Software module clustering is to divide the complex software system into many subsystems to enhance the intelligibility and maintainability of software systems. To increase convergence speed and optimize clustering solution,density PSO-based( DPSO) software module clustering algorithm is proposed. Firstly,the software system is converted into complex network diagram,and then the particle swarm optimization( PSO) algorithm is improved.The shortest path method is used to initialize the swarm,and the probability selection approach is used to update the particle positions. Furthermore,density-based modularization quality( DMQ) function is designed to evaluate the clustering quality. Five typical open source projects are selected as benchmark programs to verify the efficiency of the DPSO algorithm. Hill climbing( HC) algorithm,genetic algorithm( GA),PSO and DPSO algorithm are compared in the modularization quality( MQ) and DMQ. The experimental results show that the DPSO is more stable and more convergent than the other three traditional algorithms. The DMQ standard is more reasonable than MQ standard in guiding software module clustering.
基金The research is supported by the Ministry of Science and Technology of China under Grant No.2006CB503905Some authors are also supported by the National Natural Science Foundation of China under Grant Nos.10631070 and 10701080the JSPS(Japan Society for the Promotion of Science)-NSFC(National Natural Science Foundation of China) collaboration project under Grant No.10711140116
文摘This paper discusses a popular community definition in complex network research in terms of the conditions under which a community is minimal, that is, the community cannot be split into several smaller communities or split and reorganized with other network elements into new communities. The result provides a base on which further optimization computation of the quantitative measure for community identification can be realized.
